Select the correct answer.
What is the justification for step 4 in the solution process?
Step 1 : [tex]\frac{9}{2} b+11-\frac{5}{6} b=b+2[/tex]
Step 2 :
Step 3 :
Step 4 : [tex]\frac{22}{6} b+11=b+2[/tex]
[tex]\frac{8}{3} b+11=2[/tex]
[tex]\begin{aligned}\frac{8}{3} b & =-9 \\b & =-\frac{27}{8}\end{aligned}[/tex]
A. the multiplication property of equality
B. combining like terms
C. the addition property of equality
D. the subtraction property of equality
Answer (2)
To isolate the term with b in the equation 3 8 b + 11 = 2 , we subtract 11 from both sides. This gives us 3 8 b = − 9 . The justification for this step is the subtraction property of equality. D
Explanation
Analyzing the Problem We are given the equation 2 9 b + 11 − 6 5 b = b + 2 and asked to determine the justification for step 4 in the solution process. The steps are as follows:
Step 1: 2 9 b + 11 − 6 5 b = b + 2 Step 2: 6 22 b + 11 = b + 2 Step 3: 3 8 b + 11 = 2 Step 4: 3 8 b = − 9 b = − 8 27
Isolating the Variable Term To get from Step 3 to Step 4, we need to isolate the term with b on one side of the equation. Step 3 is 3 8 b + 11 = 2 . To isolate the term with b , we subtract 11 from both sides of the equation: 3 8 b + 11 − 11 = 2 − 11 3 8 b = − 9 This matches Step 4.
Applying Subtraction Property of Equality Since we subtracted 11 from both sides of the equation, this is an application of the subtraction property of equality, which states that if a = b , then a − c = b − c for any c .
Conclusion Therefore, the justification for step 4 is the subtraction property of equality.
Examples
The subtraction property of equality is a fundamental concept in algebra and is used extensively in solving equations. For example, if you are managing a budget and need to determine how much you can spend after paying your bills, you use subtraction to find the remaining amount. If you have a total income of $2000 and your bills are $1200, you subtract $1200 from $2000 to find that you have $800 left to spend. This is a direct application of the subtraction property of equality.
The justification for step 4 in the solution process is based on the subtraction property of equality. By subtracting 11 from both sides of the equation, we isolate the term containing b . Therefore, the answer is D: the subtraction property of equality.
;
